derivative of 5xsqrt(64-x^2)

解答

\frac{d}{d x} (5 x 64 - x^{2})

\frac{5 ( - 2 x ^{2} + 64 )}{64 - x ^{2}}

求解步骤

\frac{d}{d x} (5 x 64 - x^{2})

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 \frac{d}{d x} (x 64 - x^{2})

使用微分乘法定则:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = 64 - x^{2}

= 5 (\frac{d x}{d x} 64 - x^{2} + \frac{d}{d x} (64 - x^{2}) x)

\frac{d x}{d x} = 1

\frac{d}{d x} (64 - x^{2}) = - \frac{x}{64 - x ^{2}}

= 5 (1 \cdot 64 - x^{2} + (- \frac{x}{64 - x ^{2}}) x)

化简

5 (1 \cdot 64 - x^{2} + (- \frac{x}{64 - x ^{2}}) x) : \frac{5 ( - 2 x ^{2} + 64 )}{64 - x ^{2}}

= \frac{5 ( - 2 x ^{2} + 64 )}{64 - x ^{2}}

p a r t ia l f r a c t i o n \frac{x}{1 - x ^{2}}

f (x) = 8 x

\frac{d}{d x} (lo g_{3} (x e^{x}))

t an g e n t y = (x^{3} - 4 x)^{8}, (2, 0)

\frac{d}{d t} (\frac{e ^{t b} - e ^{t a}}{t ( b - a )})